The present invention relates to a pump, in particular a vane cell pump for supplying transmission oil, having a pump housing and a rotating group which is situated in the pump housing, the rotating group having a side plate which may be situated in the pump housing in such a way that, at least temporarily, an axial gap occurs between the side plate and the pump housing, a shaft is mounted in the pump housing and a radial packing ring is situated in a recess around the shaft. The axial gap establishes a bypass between a suction pressure area, which is represented by the suction pockets in the side plate and a corresponding area in the pump housing, and a leak oil pressure area which extends around the shaft in the rotor area.